Here, \(\Delta \omega \equiv \Omega -\omega \)  is the optical detuning, \(\imath \delta \)  denotes the homogeneous broadening, \(\langle M|J_k|M^{\prime }\rangle \)  are the matrix elements of the operator of \(k\) -th projection of the angular momentum \(F\)  [1]}, and the summation over \(M,M^{\prime }\) , and \( M^{\prime \prime }\)  is performed over \(2F+1\)  states of the ground-state multiplet.
As has been noted above, the tensor \(\alpha \)  depends on time (through the matrix elements \(\langle 1M|\rho _0|1M^{\prime }\rangle \) , see Eq. (REF )), with characteristic frequencies of this dependence corresponding to spectral features of the noise spectra observed in the SNS.
